Methods and apparatus for improving plant growth

ABSTRACT

A mechanical device including two concentric space frame structures is used to enhance plant growth. Essentially identical in shape but with the inner space frame smaller than the outer by a 4:5 relationship the space frame structures independently rotate about a common axes line. Each space frame consists of a right square pyramid of rods with its apex pointing upward and a second similar pyramid directly below it by a distance approximately two and one half times the length of each rod comprising the pyramid. The second, lower pyramid however has its apex pointing downward and is turned 45-degrees about a line connecting the two apex points. Eight additional rods complete each space frame. They each, respectively connect a corner of the upper pyramid base to a corner of the lower pyramid base in a manner that is symmetric.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of PCT US2010/001866filed Jun. 29, 2010 designating the U.S. and claims priority from U.S.provisional application 61/269,779 filed Jun. 29, 2009. These twoapplications are both hereby incorporated herein by reference in theirentirety.

FIELD

These teachings involve equipment and methods for horticultural andagricultural productivity enhancement.

BACKGROUND

The field of cultivating plants has spurred technological advances fromthe plow, to artificial irrigation, to hybridization and now to advancesin the application of DNA research. In the area of subtle influencesthat alter a plants environment, some have experimented with “talking totheir plants” and playing Mozart for them. While neither of thosetechniques has found widespread use, there is a growing body of seriousresearch regarding the effects of sound and vibrations on plant growth.Like all living organisms, plants have highly complex sensory networksfor monitoring their surroundings, and are known to modify their growthand development to suit their environment. For example, plants exposedto a variety of mechanical perturbations, such as wind or touch, undergophysiological and developmental changes that enhance resistance tosubsequent mechanical stress. Developmental changes in response tomechano-stimulation are collectively known as thigmomorphogenesis.

The short paper “Biochemical and physiological changes in plants as aresult of different sonic exposures” by Yu-Chuan Qin, Won-Chu Lee,Young-Cheol Choi and Tae-Wan Kim that was published in Elsevier'sUltrasonics journal (41 (2003) 407-41) investigates the biochemicalmechanisms that might be involved in some of these phenomena. Chinesecabbage and cucumbers at two growth stages were the researchers'subjects. For each plant type three groups were constituted. Besides acontrol group that was not subject to any artificial acoustic treatment,one group was exposed to steady ultrasonic (US) waves of 20 k Hz, whilethe other was exposed to so-called “green music” (GM) consisting of acombination of classical music and natural sounds including bird songs.Both O₂ intake and polyamines content were measured. In brief, theyfound Chinese cabbage reacting more positively to the GM and thecucumbers to the US. However, for each quantity measured, either one orthe other or both of the sonically exposed plants had greater readingsthan those of the control plants. That paper's charts of the polyaminescontent measurements are reproduced as FIGS. 1A and 1B. The caption ofthe Chinese cabbage growth graph in that paper is:

-   -   “Polyamine content (nmol/gFW) of Chinese cabbage seedlings: (A)        15 d and (B) mature plant (70 d) as a result of different        acoustic exposures. Error bars represent the standard deviations        of the means of polyamine contents.” And the caption in that        paper of the cucumber data is: “Polyamine content (nmol/gFW) of        cucumber seedlings: (A) 15 d and (B) mature plant (70 d) as a        result of different acoustic treatments. Error bars represent        the standard deviations of the means of polyamine contents.”

Studies have also focused on specific frequencies' effects, for example“Plant gene responses to frequency-specific sound signals”, Mi-JeongJeong, Chang-Ki Shim, Jin-Ohk Lee, Hawk-Bin Kwon, Yang-Han Kim,Seong-Kon Lee, Myeong-Ok Byun and Soo-Chul Park. (Mol Breeding (2008)21:217-226) published Springer's Molecular Breeding journal. Theydemonstrated sound affecting plant growth through mRNA expressionanalyses.

Others have looked at the issue of the effect of vibration on plantgrowth. One relevant article is: “Growth Promotion by Vibration at 50 Hzin Rice and Cucumber Seedlings”, Hideyuki Takahashi, Hiroshi Suge andTadashi Kato. (Plant Cell Physiol. 32(5): 729-732 (1991)). They lookedat the effect of 50 Hz vibration and mention that a motivation of theirstudy was the issue that motors and other mechanical apparatus in agreen house might produce sounds with unintended and unexpected effectson plants.

FIG. 3 shows a reproduction of that paper's “FIG. 1.” Its caption is:

-   -   “Germination of rice and cucumber seeds as affected by vibration        at 50 Hz Data is shown as the percentage of germinated seeds in        a time-course study. Top (A), rice seeds under submerged        conditions; middle (B), rice seeds on filter paper; bottom C),        cucumber seeds on filter paper. Open (◯) and closed (●) circles        indicate the control and the vibrated seeds, respectively. One        hundred seeds were used for each treatment.”

U.S. Pat. No. 7,600,343 dated Oct. 13, 2009 by Reiner Schultheiss, etal, discusses the effect of shock waves on plant growth.

However, previous attempts to improve plant growth along the lines ofthe research above have not made it into routine, large-scale,commercial use. Systems and methods are needed which can improve plantgrowth in ways compatible with our current environmental imperativesthat are also inexpensive to deploy and maintain. Preferably, solutionswould avoid chemical fertilizers and chemical pesticides and be simpleto deploy in both the developed world and the developing world.

SUMMARY

System and methods consistent with these teachings involve twocounter-rotating geometric space frame structures that may be thought ofas concentric. When energized and operated proximate to growing plants,the growth rate of those plants can be enhanced. Experimental resultshave shown its operation to be associated with effective increase inplant growth.

BRIEF DESCRIPTION OF DRAWINGS

FIGS. 1A and 1B together constitute a re-drawing of FIG. 1 of the paperof Yu-Chuan Qin, et al;

FIGS. 2A and 2B together constitute a re-drawing of FIG. 2 of the paperof Yu-Chuan Qin, et al;

FIG. 3 is a re-drawing of FIG. 1 of the paper of Hideyuki Takahashi, etal;

FIG. 4 shows a perspective view of the first example embodiment;

FIG. 5 shows a perspective view of upper and lower pyramids of the innerarmature of the unit of FIG. 4 in isolation;

FIG. 6 shows a plan view of the armature components of FIG. 5;

FIG. 7 shows a perspective view of the inner armature from theperspective view as in FIG. 5;

FIG. 8 shows the apparatus of FIG. 7 and shows an identical but largerouter armature;

FIG. 9 shows the inner armature of FIG. 7 with the larger pyramids ofthe outer armature arranged above and below it;

FIG. 10 shows a unit of the second embodiment version;

FIG. 11 shows a schematic diagram of a tomato field in which experimentswere performed noting location of the test area;

FIG. 12 is the test area of FIG. 11 expanded to show the physicallocation of test plants and equipment in the test area;

FIG. 13 is a graph showing the number of tomatoes as a function ofdistance from the unit;

FIG. 14 is the same data as seen in FIG. 13 displayed 2-dimensionally asrelative to its position in the field;

FIG. 15 shows tomato growth using an indoor unit;

DETAILED DESCRIPTION

Introduction

The global population is estimated to reach 9 billion people by 2050.There is an increasing loss of arable land caused by desertification anddecreasing water supplies caused by melting glaciers and erraticprecipitation patterns. It may be difficult to feed the world'spopulation in the future. Equipment and methods to enhance plant growthare therefore of high global importance.

Structure

In a first example embodiment seen in FIG. 4, a machine includes aplatform 100 supporting a vertical axle 101. Rotatably coupled to theaxle are an inner armature 102 and an outer armature 103. Each of thesearmatures is supported by respective bearings 104 and are arranged toseparately, freely rotate about the axle. A source of motive force inthis example, are two DC motors 105 and are mechanically connected bybelt drives 106 to each armature to provide for their respectiverotation in opposite directions. In this first example device, the outerarmature 103 revolves clock-wise with the inner armature 102 goingcounter-clockwise. The relative rotation of the armatures is not set toa fixed relationship by mutual gearing, for example. The motors arecapable of being adjusted to cause each armature to rotate in a range of400 to 500 rotations per minute. In this example the upper surface ofthe top supports a solar cell panel 402 that provides the energy tooperate the motors. Those skilled in the art will be familiar with thespecific current requirements of various motors that may be used and theenergy storage than may be required. In this example the electricityfrom the solar panels is used to charge batteries. The motors, under thecontrol of a timer and speed controllers, is then driven from thebatteries.

Armatures

The inner and outer armatures of this version are each a geometric frameconstructed from stainless steel rods. Aluminum rods may also be used.The armatures are of the same geometric configuration with thedifference being that the outer armature 103 is a scaled up instance ofthe configuration of the inner armature 102. Therefore the innerarmature will be initially described in isolation. This also allows forclearer drawings than those showing the entire machine.

Inner Armature

Its height is the dimension that would be from its top to its bottomwhen configured on the axle on the platform in a usage configuration. Inthis first version the inner armature's 102 overall height, is about28.5 inches. The upper-most and lower-most elements are rods of adiameter of about ⅜″, centered within the armature body that fits overthe axle. The armature can be thought of as a space frame with its topand bottom portions being symmetrically arranged rectangular, rightpyramid space frames. To allow this description to be more meaningful,the lengths of the space frame rods will be expressed in relation to thelength (L) of the rods that make up the upper and lower pyramids. Forthis inner pyramid L is 9″. As seen in FIG. 5, the upper, inner pyramid121 has a base 122 that is formed by four rods of length L 128 arrangedto represent the sides of a square. From each corner 223 224 225 226 ofthat base is a rod 129 representing a vertex of the pyramid. The rods'other ends all meet near an apex 126. In this case the vertices rods'are also of length L. These identical lengths of base and vertexsegments result in a shape with faces that are at about 52 degrees tothe plane of the base.

The upper pyramid, 121 as mentioned, is complimented by an identicallower pyramid 130 that is of an identical space frame configuration.However, in constituting the armature, the lower pyramid has its apex136 pointing downward. Its position is symmetric relative to the upperpyramid with the exception of being rotated by 45 degrees about a lineconnecting the two apex points 126 136. This rotational offset is betterseen in FIG. 6 that shows a top plan view of the pyramids of FIG. 5.

As seen in FIG. 7 as well as other figures, the two pyramids are spacedapart by connecting rods 131 that interconnect the corners of the upperpyramid's base 122 with corners of the lower pyramid's base 133. Eachcorner is connected to the two nearest corners of the opposing pyramid'sbase. For example, a particular corner of the upper pyramid 224 has oneattached connecting rod 131 whose other end is attached to corner 235 ofthe lower pyramid 130. A second connecting rod is attached to the sameupper pyramid corner 224 and its other end is attached to the lowerpyramid at a second corner 234. The six remaining connecting rods aresimilarly attached to the pyramids creating the symmetric geometricshape of the inner armature. Since the pyramids are rotationally offset,these eight equal length rods take a form of the letter “V”. In thisexample, the length of those rods are all of length 1.8*L. Theconsequence to these relative rod dimensions is that the height of thepyramids is 0.707*L while the distance between bases is 0.95*L. Thetotal length from apex to apex is therefore (2*1.8+0.95)*L or 3.1*L. Asmentioned, the pyramids' respective vertices meet near the apex. Infact, they terminate at the upper and lower support tubes 127 137respectively. These support tubes are centered on the armature'sapex-to-apex centerline.

FIG. 8 shows an inner armature surrounded by an outer armature, both ona common axle through their support tubes. In this version, the outerarmature has rods making up its pyramids that are length 11 inches.Bearings support the armatures for rotating on the axle. They providefor independent driving of each armature in their respective rotations.The total height of the dual armature assembly is about 36 inches fromapex to apex.

Assembly Method

The various rods and pipes that make up most parts of the armatures arewelded together in this first example. Since one is completely inside ofthe other, the outer armature is welded together after being assembledaround the inner armature. FIG. 9 shows a partially assembled unit. Theouter upper and lower pyramids are in place surrounding the innerarmature. The next step would be to weld the outer armature's connectingrods to the appropriate corner locations on the two large pyramids.

Variations

While a solar powered unit may be ideal for field use, motors running onAC mains power might be more suitable for use in a green house or in anindoor hydroponic application. Rather than having a motor for eacharmature, it is known to those skilled in the art to use a single motorwith gearing or other mechanical coupling to have one motive source turnthe armatures in opposite directions. The entire unit may be scaled upor scaled down, keeping the proportions constant.

Second Example Embodiment

A similar geometric shape to the first example unit is present in thesecond example embodiment. However, the second embodiment is intendedfor indoor use. The armatures rods are each one half the total length ofthe corresponding structure in the first example. This version is shownin FIG. 10. Rather than a platform and pipes to support it, this unit isin a self-contained cabinet.

Operation

For outdoor operation the embodiment of example one can be supportedfrom the ground by 2-inch galvanized pipes approximately one foot intothe ground that support the platform near its four corners. The unit isplaced in a field in proximity to the crops to be effected. The solarpanel is connected to a battery that, in turn, is connected to a timerand to speed controllers for the two motors. The timers are recommendedto be set to operate the apparatus three to five times during daylighthours at equally spaced intervals for equal durations. An exampleoperation is operating for five minutes, three times a day, at intervalsthat split the daylight hours into four segments. Since the sunlightavailable is variable, those skilled in the art will recognize thefunction of the battery in providing a steady source of energy to rotatethe armatures at a predetermined rate for a predetermined duration. Therate for each armature respectively can be between 400 and 500revolutions per minute.

Alternate Modes of Operation

A smaller, indoor unit is bolted to the floor the plants are restingupon. Alternatively it is bolted to a wall that is, in turn, abuttingand secured to that floor. An indoor unit would most likely be poweredfrom AC, as mentioned.

AC could also power an outdoor unit. Other modes of powering could be awind turbine substituting for the solar panels. Another could involvederiving power from the flow of water in an irrigation system.

Experiments to-Date

Outdoors Experiment

Two primary experiments have been performed. A large-scale outdoor trialwas performed at Eclipse Farms in the City of Oxnard, Calif. The cropgrown there is Roma tomatoes. A unit 600 constructed as the firstexample embodiment was installed and operated as discussed in theoperation section above in a 35-acre rectangular field 500. Within thefield a square of 10 acres 700 (660 feet per side) had a unit placed atits center. Plant locations were marked off along lines due North, East,South and West from the center location to the perimeter of the square.The unit was activated on Jul. 20, 2009 and controlled by the inventorduring the testing.

In FIG. 12 the location of five plants per line were marked as plants tobe measured in the experiment. Starting from the unit (in eachrespective compass point direction) the distances from the center were50 feet, 100 feet, 175 feet, 225 and 330 feet. In addition there werefour other plants marked for testing. These four plants were along thesame four lines at the four points at which respective line intersectsthe acre plot perimeter. In FIG. 11 these points are designated A, B, Cand D. The 20 plant locations within the square are designated in FIG.12. The five “West” plant locations are designated W1, W2, W3, W4 andW5. The “East” plant locations are designated E1, E2, E3, E4, and E5 andso on for the North and the South.

The twenty-four marked test plants were measured for over fourteenweeks. Those measurements included counting the tomatoes each week. Inaddition, in the first few weeks, both the number of flowers and thenumber of tomatoes were counted twice a week.

Results

The number of tomatoes in the twenty locations on the E-W and N-S lineswithin the 10 acres is shown in FIG. 13 as a line graph. That figureshows the N 301, S 302, E 303 and W 304 tomato counts as a function offeet from the unit. Also seen is a curve representing the average 305.This graph demonstrates a fall off of the effect of the unit withdistance which is consistent with many physical phenomena. The same datais displayed in a three-dimensional format in FIG. 14. The X and Ypositions represent the plants' location relative to the unit. The Zheights represent the number of tomatoes on the plant at that locationwhen counted at the end of the experiment.

It can be seen that in all directions there is a general falling off oftomato count as distance from the unit increases.

The other four tomatoes were not at constant distances from the unitsince the overall field is rectangular. A and C are at 460 feet, B is at270 feet, D is at 20 feet. Those data points are also included in thegraph of FIG. 13.

Indoors Experiment

A second set of experiments were performed indoors. In fact it was on abalcony of an apartment in Marina Del Rey, Calif. These experiments wereperformed during 2008. The tests used different plants includingCelosia, Tomatoes, and Pepper plants. The plants were sourced in twosfrom a nearby Home Depot. Plants of similar height and girth werechosen. If one was arguable slightly larger than the other, that one wasmade the control plant.

The procedure was that the potted plants were placed a few inches aparton a table on the balcony. Lab calibrated beakers were obtained and usedto measure water and nutrients that were applied equally to both plants.Every week the plants positions were changed to account for anydifference in sunlight.

Each day the test plant was taken to another room inside where a Biowaveunit was bolted to the wall. The motors of this machine were set a yardaway from the machine itself (to be further from the plant) so that anymagnetic field from the motors would not impact on the plants. Also themotors were screened with expanded metal and grounded to further reduceany EM radiation. This was measured with a magnetometer.

The test plant was placed beside the machine for 15 minutes a day andthen returned to the balcony. In one test run the test plant had 15blossoms, while the control plant had 7 blossoms. This experiment wasrepeated at least 18 times during 2008 with both with of the otherplants. All of the tests showed the test plants with greater growth thanthe control plants.

Four of the 18 tests were with organic tomatoes. In all these cases thetest plant to control plant tomato-count ratio ranged from 4 times to 2.The results of one particular test run are shown in FIG. 15. The moredensely hatched columns represent the number of tomatoes on the testplant. The other columns represent the control plant. Both are plottedat one week intervals over seven weeks. Additionally, in at least onedocumented test run, the test plant also had significantly less insectdamage than the control plant.

A tomato from one of the experiment's test plants was analyzed for itsBrix content by Silliker Labs of Cypress Calif. The USDA average Brixrating for an organic tomato is 4.9%. The tests performed by thisindependent lab showed the test tomatoes to have a Brix rating of 10.5%.

Theory of Operation

No particular theory of operation is presented or known. Various knownmechanisms may be involved including acoustic waves transmitted throughthe air or vibrations transmitted through the ground. Gravity is anotherpossible communication medium. The papers mentioned in the backgroundsection, “Biochemical and physiological changes in plants as a result ofdifferent sonic exposures” by Yu-Chuan Qin, Won-Chu Lee, Young-CheolChoi and Tae-Wan Kim and “Growth Promotion by Vibration at 50 Hz in Riceand Cucumber Seedlings”, by Hideyuki Takahashi, Hiroshi Suge and TadashiKato. (Plant Cell Physiol. 32(5): 729-732 (1991)). These and otherpublications evidence serious researchers studying possiblynot-yet-understood factors that can affect plant health and growth.

Publications that teach subtle influences on plant growth include,“Plant gene responses to frequency-specific sound signals” Mi-JeongJeong, Chang-Ki Shim, Jin-Ohk Lee, Hawk-Bin Kwon, Yang-Han Kim,Seong-Kon Lee, Myeong-Ok Byun and Soo-Chul Park., “Growth of theCellular Slime Mold, Dictyostelium discoideum, Is Gravity Dependent”Yukishige Kawasaki*, Takeshi Kiryul, Kenji Usui1, and Hiroshi Mizutani,Mitsubishi-Kasei Institute of Life Sciences, 11 Minamiooya, Machida,Tokyo 194, Japan. Another paper showing an effect of music and even lesstangible inputs causing differences in plant growth is “MeasuringEffects of Music, Noise, and Healing Energy Using a Seed GerminationBioassay” From the journal of alternative and complementary medicineVolume 10, number 1, 2004, pp. 113-122 Katherine Creath, Ph.D. (OpticalScience), Ph.D. (Music), 1-3 And Gary E. Schwartz, Ph.D.1, 3.

Still other scholarly papers that may be relevant are from Plant andCell Physiology, 2002, Vol. 43, No. 6 647-651. “Effects of MechanicalVibration on Seed Germination of Arabidopsis thaliana” (L.) Heynh. AyuhoUchida1, 3 and Kotaro T. Yamamoto 1, 2, 4. and 1. J Gravit Physiol. 1996April; 3(1):69-74. Also, “Gravity related features of plant growthbehavior studied with rotating machines”. Brown A H. Collaborators:Brown A H. University of Pennsylvania (Philadelphia), USA.

Those skilled in the art will recognize that these and other teachingssuggest that occurrences proximate to plants may have effects on theirgrowth even though the mechanisms may not be understood. They representserious researcher's efforts to understand subtle influences on plantgermination and growth.

These seven papers mentioned above are hereby incorporated by referencein their entirety. In particular, FIGS. 2A and 2B are reproductions ofcharts appearing in the paper “Biochemical and physiological changes inplants as a result of different sonic exposures” mentioned above. FIG.2A shows polyamine content (nmol/gFW) of cucumber seedlings. FIG. 2Bshows a mature plant with a different acoustic treatment. Error barsrepresent the standard deviations of the means of polyamine contents. Itcan be seen from these figures that the polyamine uptake is greatest inthe plants exposed to ultrasound.

Various embodiments with various modifications as are suited to theparticular use contemplated are expected. In the following claims, thewords “a” and “an” should be taken to mean “at least one” in all cases,even if the wording “at least one” appears in one or more claimsexplicitly. The scope of the invention is set out in the claims below.

What is claimed:
 1. A mechanical apparatus for treating plantscomprising: a. a base; b. an inner space frame armature, c. an outerspace frame armature of a shape geometrically similar to said innerspace frame armature and scaled larger than said inner space-framearmature; further, said inner armature being substantially containedwithin said outer armature, the inner space frame being scaled down inproportion to the first space frame at a ratio of about 5:4; d. an axle,said axle being supported from said base in a vertical orientation withsaid outer armature rotatably disposed about said axle; e. a motivesource operatively coupled to said inner armature and; f. a motivesource operatively coupled to said outer armature; said motive sourcesso constituted and configured and coupled to said respective armaturesas to engender said armatures to rotate about the line of said axle inmutually opposite directions when said motive sources are energized andactivated, the rotation of the armatures generating acoustic waves;further, said armatures each comprise rods constituting the space framein the form of a set of geometric shapes including an upper and a lowerright square pyramid disposed with their respective bases in parallelplanes and their apexes such that a line through the apex points wouldbe perpendicular to the planes of their bases; still further, thepyramids are mutually spaced apart and rigidly connected to each otherby two rods extending from each corner of the upper pyramid to the tworespective closest corners of the base of the lower pyramid.
 2. Theapparatus of claim 1 wherein said at least one motive source comprisesan electric motor.
 3. The apparatus of claim 1 wherein said at least onemotive source comprises a DC motor.
 4. The apparatus of claim 1 whereinsaid at least one motive source comprises wind power.
 5. The apparatusof claim 1 wherein said motive source comprises an AC motor.
 6. Theapparatus of claim 3 further comprising a solar panel operativelycoupled to said motors such as to provide energy for said motors.
 7. Theapparatus of claim 3 wherein the source for energy for the motive forcecomprises waterpower.
 8. The apparatus of claim 1 wherein the motivesource operatively coupled to said inner armature is distinct from themotive source operatively coupled to said outer armature.
 9. Theapparatus of claim 1 so configured as to permit rotational rates ofbetween 250 and 1000 revolutions per minute.
 10. The apparatus of claim1 wherein one or more of the rods are substantially composed of amaterial from the list consisting of stainless steel and aluminum. 11.The machine of claim 1, wherein the mutual alignment of said pyramids issuch that a side of the base of the upper pyramid is at a 45-degreeangle to a side of the base of the lower pyramid.
 12. A method oftreating plants comprising: providing a specific symmetric geometricconfiguration in the presence of plants; a. rotating a first verticalspace frame, of the specific symmetric geometric configuration, aboutits vertical center line; b. rotating a second vertical space frame ofsubstantially the same shape as the first space frame and that has acommon center line with the first vertical space frame, wherein thesecond space frame is scaled down in proportion to the first space frameat a ratio of about 5:4; wherein the rotation of the first verticalspace frame and the rotation of the second space frame are in oppositedirections, the rotation of the space frames generating acoustic waves;and wherein the specific symmetric geometric configuration has thefollowing properties: i. rotationally symmetric with 4-fold symmetryabout its vertical center line; ii. includes congruent, opposed,geometric configurations at its upper and lower extremities.
 13. Themethod of claim 12 wherein the space frames of the specific symmetricgeometric configuration comprise a set of geometric shapes including anupper and a lower right square pyramid disposed with their respectivebases in parallel planes and their apexes such that a line through themwould be perpendicular to the planes of their bases; further, the mutualalignment of said pyramids is such that a side of the base of the upperpyramid is at a 45-degree angle to a side of the base of the lowerpyramid; still further, the pyramids are mutually spaced apart andrigidly connected to each other by two rods extending from each cornerof the upper pyramid to the two respective closest corners of the baseof the lower pyramid.
 14. The method of claim 12 wherein the respectiverotational rates are each between about 400 and 500 revolutions perminute.
 15. The method of claim 12 wherein the ratio of rods comprisinga pyramid to rods connecting pyramids to each other is about betweenabout 1:1.8 and 1:2.
 16. The method of claim 12 wherein at least one ofthe rotational rates is between about 400 and 500 revolutions perminute.
 17. The method of claim 12 wherein at least one of therotational rates is between about 100 and 2000 revolutions per minute.18. The method of claim 12, wherein the congruent, opposed,configurations are square right pyramids.